LORENTZ MATRICES - A REVIEW

This is an expository review of the Lorentz transformation, which is a change of coordinates used by one ''inertial observer'' to those used by another one. The transformation can be represented by a four-by-fo ur matrix, the Lorentz matrix or the Minkowski-Lorentz matrix. The mos t familiar, or ''special,'' case has the x axis of both observers para llel to their relative velocity. A more general transformation drops t his constraint. But then a seeming ''paradox'' arises when there are t hree observers, and this has led to a challenge to the self-consistenc y of the special theory of relativity. It is shown here that this chal lenge is based on a misunderstanding. The properties of the more gener al Lorentz transformation are reviewed consistently in terms of the ma trix approach, which the author believes is now the easiest approach t o understand. The spectral analysis of the Lorentz matrix is also disc ussed. Several checks are included to ''make assurance double sure.''